Designing Frequency-Dependent Impedances?

Hi,
Every one knows, that e.g. a simple RC-parallel circuit has a
frequency-dependent impedance-characteristic (Absolute Value) - the
impedance (Abs) raises as the Frequency approaches zero. As a formula: Zin
= 1/(1/R + i w C) , where i ist the imaginary number and w the frequency.

Now the hard part. How does one create an Impedance, which decreases
"slower", for frequencies close to zero but then decreases "faster" for
higher frequencies, than the simple parallel RC-Circuit?
Is there some kind of procedure like the one for syntesizeing LC-Filters
(Butterworth, Chebychev,..)?

Simply increasing C does not really help, because this equals a factoring of
the frequency.
Increasing R does not help as well, as it seems.

I hope one of you cracks can help me out.
So far, thanks for reading.
Diego Stutzer

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"Diego Stutzer" <> wrote in message
news:...
> Hi,
> Every one knows, that e.g. a simple RC-parallel circuit has a
> frequency-dependent impedance-characteristic (Absolute Value) - the
> impedance (Abs) raises as the Frequency approaches zero. As a formula:
Zin
> = 1/(1/R + i w C) , where i ist the imaginary number and w the frequency.
>
> Now the hard part. How does one create an Impedance, which decreases
> "slower", for frequencies close to zero but then decreases "faster" for
> higher frequencies, than the simple parallel RC-Circuit?
> Is there some kind of procedure like the one for syntesizeing LC-Filters
> (Butterworth, Chebychev,..)?
>
> Simply increasing C does not really help, because this equals a factoring
of
> the frequency.
> Increasing R does not help as well, as it seems.
>
>
> I hope one of you cracks can help me out.
> So far, thanks for reading.
> Diego Stutzer

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If you think of it as a "filter", you may be able to find software
that lets you specify values at frequencies, and will design a network
for you. But if I understand correctly, you simply want an impedance
whose magnitude is some value at some mid frequency, and drops above
and below that. That's just a parallel LRC circuit. If you need the
impedance to go to (or near) zero at some specific high frequency, you
can put an LC series across the parallel LRC. Actually, you can do it
by making the C an LC series instead. But then the impedance rises
again beyond the LC series resonance.

It can be a useful visualization to think of poles and zeros in the
s-plane when trying to get to a circuit that gives you a specific
impedance shape. You can readily see that some responses are not
possible with a finite number of L/R/C components, though in general
you can get the impedance magnitude you want at a set of distinct
frequencies with a finite number of _ideal_ components. I'll bet
there are some good s-plane pole/zero tutorials on the web.

Cheers,
Tom

(Diego Stutzer) wrote in message news:<>...
> Hi,
> Every one knows, that e.g. a simple RC-parallel circuit has a
> frequency-dependent impedance-characteristic (Absolute Value) - the
> impedance (Abs) raises as the Frequency approaches zero. As a formula: Zin
> = 1/(1/R + i w C) , where i ist the imaginary number and w the frequency.
>
> Now the hard part. How does one create an Impedance, which decreases
> "slower", for frequencies close to zero but then decreases "faster" for
> higher frequencies, than the simple parallel RC-Circuit?
> Is there some kind of procedure like the one for syntesizeing LC-Filters
> (Butterworth, Chebychev,..)?
>
> Simply increasing C does not really help, because this equals a factoring of
> the frequency.
> Increasing R does not help as well, as it seems.
>
>
> I hope one of you cracks can help me out.
> So far, thanks for reading.
> Diego Stutzer

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